Monomials, Binomials, and Riemann-Roch
نویسندگان
چکیده
The Riemann-Roch theorem on a graph G is closely related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration. We also develop a self-contained Riemann-Roch theory for artinian monomial ideals.
منابع مشابه
Indispensable monomials of toric ideals and Markov bases
Extending the notion of indispensable binomials of a toric ideal ((14), (7)), we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for searching indispensable binomials of a toric ideal and for proving the existence or non-existence of a unique minimal system of binomials generators of a toric ideal. Some examples of indispensable monomials ...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Indispensable monomials of toric ideals and Markov bases
Extending the notion of indispensable binomials of a toric ideal ([14], [7]), we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for searching indispensable binomials of a toric ideal and for proving the existence or non-existence of a unique minimal system of binomials generators of a toric ideal. Some examples of indispensable monomials ...
متن کاملA New Family of Perfect Nonlinear Binomials
We prove that the binomials xp s+1 − αxpk+p2k+s define perfect nonlinear mappings inGF (p3k) for appropriate choices of the integer s and α ∈ GF (p3k). We show that these binomials are inequivalent to known perfect nonlinear monomials. As a consequence we obtain new commutative semifields for p ≥ 5 and odd k.
متن کاملJ an 2 00 7 GRAPHS , ARITHMETIC SURFACES , AND THE RIEMANN - ROCH THEOREM
We use the theory of arithmetic surfaces to show that the Riemann-Roch theorem for Q-graphs is a direct consequence of the usual Riemann-Roch theorem for curves in algebraic geometry.
متن کاملRiemann-roch for Deligne-mumford Stacks
We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory, together with some basic commutative algebra of Artin local rings.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1201.4357 شماره
صفحات -
تاریخ انتشار 2012